基于约束总体最小二乘方法的到达时差到达频差无源定位算法

两步加权最小二乘方法(two-stage WLS)是求解TDOA/FDOA无源定位问题的经典线性方法，但也存在着定位偏差和均方误差对测量噪声的适应能力较差的缺点。该文根据TDOA/FDOA的伪线性定位方程组特点，将其建立为一种带约束条件的约束总体最小二乘(CTLS)模型，并采用拉格朗日乘子法求解带约束条件的CTLS问题，建立了几种最小二乘类定位方法的统一解，从而将约束加权最小二乘(CWLS)定位解和约束最小二乘(CLS)定位解变为该文CTLS定位解的特例。仿真表明，该文方法比两步加权最小二乘方法具有更低的均方误差，并能够有效减小定位偏差，因而具有更好的测量噪声适应能力。

Source Localization Using TDOA and FDOA Measurements Based on Constrained Total Least Squares Algorithm

The two-stage Weighted Least Squares (WLS) method is a well-known linear approach in Time- Difference-Of-Arrival (TDOA) and Frequency-Difference-Of-Arrival (FDOA) passive localization. But this method can only attain the CRLB in a modest noise environment and the bias of the localization result is significant for strong noise. This paper discusses a Constrained Total Least Square (CTLS) solution to the pseudo linear equations with two constrains for TDOA/FDOA localization. A unified expression for several LS solutions is derived based on Lagrange multiplier. The Constrained Weighted Least Square (CWLS) method and Constrained Least Square (CLS) localization method reduce to the special cases of the localization solution. The simulation results show that the proposed method has lower Mean Square Error (MSE) and lower bias compared with the two-stage WLS method, and it is more robust to noise.